How to solve equations with more unknowns

I want to write a code to find pi,pj and pk. How to solve these equations, all x and y terms are known.

Eq1 : x=pi.xi + pj.xj + pk.xk
Eq2 : y=pi.yi + pj.yj + pk.yk
Eq3 : pi + pj + pk = 1

[TADA]

seems like a system of 3 linear equations with 3 parameters. If I got it right, all you need is to declare your parameters (pi, pj, pk) as symbolic variables, and send these equations to solve function.

Have a look here: https://www.mathworks.com/help/symbolic/solve-a-system-of-linear-equations.html#bud2_az-1

[Bruno Luong]

What's that means?

pi.xi

[Awais Saeed]

TADA its working. Bruno i am doing a project on Color Shift Keying for visible light communication for which i am trying to convert chromaticity coordinates(x,y) into a 3-element vector P which is the power of LEDs and the xi and yi etc are chromaticity values at the central wavelengths of RGB LEDs.

[TADA]

@awais Saeed, I think bruno ment what do you mean by the syntax

pi.xi

I assumed you ment multiplation, which you should right like that so it is clear

pi*xi

[Walter Roberson]

Instead of solve() you can probably use the numeric \ operator.

[madhan ravi]

TADA its working.

is pi a struct with values?

[Awais Saeed]

Yes it is multiplication(pi*xi). Pi,pj,pk are variables not struct.

[Awais Saeed]

@walter roberson i have solved the equations with solve() command. But how with numeric \ operator

Answer 1

[Walter Roberson]

A = [xi, xj, xk;
     yi, yj, yk;
      1,  1,   1];
b = [x;
     y;
     1];

sol = A\b;
pi = sol(1); pj = sol(2); pk = sol(3);